I believe so too, but from a slightly different angle: I believe self-driving vehicles will literally mean the end for both Uber & Lyft (and they only accelerate their fate by investing into it).
To understand why: their inherent value is their ability to match human drivers with customers. They both do such a good job at it, that the switching costs between the 2 apps are quite low (first sign of weak competitive advantage).
Now, take away the difficult problem of finding human drivers at the right place and the right time. You now have self-driving cars that make no mistakes, have no scheduling issues, do not get tired etc. It’s way easier to fullfil demand. But, you’re not the only one working on this problem. Google, Tesla, (probably Apple too) are all actively working on the same problem. And they probably have 10X the computing/engineering/cash/data resources to solve this problem.
What are Uber/Lyft left with? A fancy app with a button (which they have already proven to easily clone). Not only that, they also have to compete with the native operating systems (and future devices) that the big corps control. They don’t even own their maps!
So yes, in 2023, you will probably be able to order a Level-5 self driving vehicle to your doorstep with a wink of your half robotic eye, but it will not be Uber or Lyft.